2n^2=24-9n

Solution for 2n^2=24-9n equation:

2n^2=24-9n

We move all terms to the left:

2n^2-(24-9n)=0

We add all the numbers together, and all the variables

2n^2-(-9n+24)=0

We get rid of parentheses

2n^2+9n-24=0

a = 2; b = 9; c = -24;
Δ = b2-4ac
Δ = 92-4·2·(-24)
Δ = 273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{273}}{2*2}=\frac{-9-\sqrt{273}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{273}}{2*2}=\frac{-9+\sqrt{273}}{4}
$